Second-order integral model for a round turbulent buoyant jet

2002 ◽  
Vol 459 ◽  
pp. 397-428 ◽  
Author(s):  
HONGWEI WANG ◽  
ADRIAN WING-KEUNG LAW
Keyword(s):  
Mass Flux ◽  
Richardson Number ◽  
Momentum Flux ◽  
Second Order ◽  
Integral Model ◽  
Width Ratio ◽  
Buoyant Jet ◽  
Turbulent Characteristics ◽  
Momentum Fluxes ◽  
Local Mean

The development of a second-order integral model for a round turbulent buoyant jet is reported based on new experimental data on turbulent mass and momentum transport. The mean and turbulent characteristics of a round vertical buoyant jet covering the full range from jets to plumes were investigated using a recently developed combined digital particle image velocimetry (DPIV) and planar laser-induced fluorescence (PLIF) system. The system couples the two well-known techniques to enable synchronized planar measurements of flow velocities and concentrations in a study area. The experimental results conserved the mass and momentum fluxes introduced at the source accurately with closure errors of less than 5%. The momentum flux contributed by turbulence and streamwise pressure gradient was determined to be about 10% of the local mean momentum flux in both jets and plumes. The turbulent mass flux, on the other hand, was measured to be about 7.6% and 15% of the mean mass flux for jets and plumes respectively. While the velocity spread rate was shown to be independent of the flow regime, the concentration-to-velocity width ratio λ varied from 1.23 to 1.04 during the transition from jet to plume. Based on the experimental results, a refined second-order integral model for buoyant jets that achieves the conservation of total mass and momentum fluxes is proposed. The model employs the widely used entrainment assumption with the entrainment coefficient taken to be a function of the local Richardson number. Improved prediction is achieved by taking into account the variation of turbulent mass and momentum fluxes. The variation of turbulent mass flux is modelled as a function of the local Richardson number. The turbulent momentum flux, on the other hand, is treated as a fixed percentage of the local mean momentum flux. In addition, unlike most existing integral models that assume a constant concentration-to-velocity width ratio, the present model adopts a more accurate approach with the ratio expressed as a function of the local Richardson number. As a result, smooth transition of all relevant mean and turbulent characteristics from jet to plume is predicted, which is in line with the underlying physical processes.

A second-order integral model for buoyant jets with background homogeneous and isotropic turbulence

2019 ◽  
Vol 871 ◽  
pp. 271-304 ◽  
Author(s):  
Adrian C. H. Lai ◽  
Adrian Wing-Keung Law ◽  
E. Eric Adams
Keyword(s):  
Isotropic Turbulence ◽  
Second Order ◽  
Integral Model ◽  
Length Scale ◽  
Buoyant Jet ◽  
Buoyant Jets ◽  
Jet Mixing ◽  
Mixing Characteristics ◽  
Background Turbulence ◽  
Homogeneous And Isotropic Turbulence

Buoyant jets or forced plumes are discharged into a turbulent ambient in many natural and engineering applications. The background turbulence generally affects the mixing characteristics of the buoyant jet, and the extent of the influence depends on the characteristics of both the jet discharge and ambient. Previous studies focused on the experimental investigation of the problem (for pure jets or plumes), but the findings were difficult to generalize because suitable scales for normalization of results were not known. A model to predict the buoyant jet mixing in the presence of background turbulence, which is essential in many applications, is also hitherto not available even for a background of homogeneous and isotropic turbulence (HIT). We carried out experimental and theoretical investigations of a buoyant jet discharging into background HIT. Buoyant jets were designed to be in the range of $1<z/l_{M}<5$, where $l_{M}=M_{o}^{3/4}/F_{o}^{1/2}$ is the momentum length scale, with $z/l_{M}<\sim 1$ and $z/l_{M}>\sim 6$ representing the asymptotic cases of pure jets and plumes, respectively. The background turbulence was generated using a random synthetic jet array, which produced a region of approximately isotropic and homogeneous field of turbulence to be used in the experiments. The velocity scale of the jet was initially much higher, and the length scale smaller, than that of the background turbulence, which is typical in most applications. Comprehensive measurements of the buoyant jet mixing characteristics were performed up to the distance where jet breakup occurred. Based on the experimental findings, a critical length scale $l_{c}$ was identified to be an appropriate normalizing scale. The momentum flux of the buoyant jet in background HIT was found to be conserved only if the second-order turbulence statistics of the jet were accounted for. A general integral jet model including the background HIT was then proposed based on the conservation of mass (using the entrainment assumption), total momentum and buoyancy fluxes, and the decay function of the jet mean momentum downstream. Predictions of jet mixing characteristics from the new model were compared with experimental observation, and found to be generally in agreement with each other.

scholarly journals Retroflection from slanted coastlines-circumventing the "vorticity paradox"

Ocean Science ◽  
2008 ◽  
Vol 4 (4) ◽  
pp. 293-306 ◽  
Author(s):  
V. Zharkov ◽  
D. Nof
Keyword(s):  
Mass Flux ◽  
Momentum Flux ◽  
Necessary Condition ◽  
System Of Equations ◽  
Maximum Value ◽  
Ring Dynamics ◽  
Momentum Fluxes ◽  
Nonlinear Analytical Model ◽  
Western Side ◽  
Westward Drift

Abstract. The balance of long-shore momentum flux requires that the solution of zonally retroflecting currents involve ring shedding on the western side. An important aspect of the ring dynamics is the ring intensity α (analogous to the Rossby number), which reaches its maximum value of unity when the upstream potential vorticity (PV) is zero. Friction leads to a slow-down and a decrease in α. The main difficulty is that the solution of the system of equations for conservation of mass and momentum of zonal currents leads to the conclusion that the ratio (Φ) of the mass flux going into the rings and the total incoming mass flux is approximately 4α/(1+2α). This yields the "vorticity paradox" – only relatively weak rings (α≤1/2) could satisfy the necessary condition Φ≤1. Physically, this means, for example, that the momentum-flux of zero PV currents upstream is so high that, no matter how many rings are produced and, no matter what size they are, they cannot compensate for it. To avoid this paradox, we develop a nonlinear analytical model of retroflection from a slanted non-zonal coastline. We show that when the slant of coastline (γ) exceeds merely 150, Φ does not reach unity regardless of the value of α. Namely, the paradox disappears even for small slants. Our slowly varying nonlinear solution does not only let us circumvent the paradox. It also gives a detailed description of the rings growth rate and the mass flux going into the rings as a function of time. For example, in the case of zero PV and zero thickness of the upper layer along the coastline, the maximal values of Φ can be approximately expressed as, 1.012+0.32exp(−γ/3.41)−γ/225. Interestingly, for significant slants γ≥300), the rings reach a terminal size corresponding to a balance between the β-force and both the upstream and downstream momentum fluxes. This terminal size is unrelated to the ultimate detachment and westward drift due to β. Our analytical solutions are in satisfactory agreement with the results of a numerical model that we run.

The Lid-Driven Cavity Flow: A Synthesis of Qualitative and Quantitative Observations

1984 ◽  
Vol 106 (4) ◽  
pp. 390-398 ◽  
Author(s):  
J. R. Koseff ◽  
R. L. Street
Keyword(s):  
Heat Flux ◽  
Flow Visualization ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Lower Boundary ◽  
Thymol Blue ◽  
Width Ratio ◽  
Cavity Depth ◽  
Driven Cavity ◽  
Turbulent Characteristics

A synthesis of observations of flow in a three-dimensional lid-driven cavity is presented through the use of flow visualization pictures and velocity and heat flux measurements. The ratio of the cavity depth to width used was 1:1 and the span to width ratio was 3:1. Flow visualization was accomplished using the thymol blue technique and by rheoscopic liquid illuminated by laser-light sheets. Velocity measurements were made using a two-component laser-Doppler-anemometer and the heat flux on the lower boundary of the cavity was measured using flush mounted sensors. The flow is three-dimensional and is weaker at the symmetry plane than that predicted by accurate two-dimensional numerical simulations. Local three-dimensional features, such as corner vortices in the end-wall regions and longitudinal Taylor-Go¨rtler-like vortices, are significant influences on the flow. The flow is unsteady in the region of the downstream secondary eddy at higher Reynolds numbers (Re) and exhibits turbulent characteristics in this region at Re = 10,000.

scholarly journals A new approach to momentum flux determinations using SKiYMET meteor radars

2005 ◽  
Vol 23 (7) ◽  
pp. 2433-2439 ◽  
Author(s):  
W. K. Hocking
Keyword(s):  
New Mexico ◽  
Momentum Flux ◽  
Middle Atmosphere ◽  
Beam Forming ◽  
New Approach ◽  
Meteorology And Atmospheric Dynamics ◽  
Momentum Fluxes ◽  
Waves And Tides ◽  
Resolute Bay

Abstract. The current primary radar method for determination of atmospheric momentum fluxes relies on multiple beam studies, usually using oppositely directed coplanar beams. Generally VHF and MF radars are used, and meteor radars have never been successfully employed. In this paper we introduce a new procedure that can be used for determination of gravity wave fluxes down to time scales of 2-3h, using the SKiYMET meteor radars. The method avoids the need for beam forming, and allows simultaneous determination of the three components of the wind averaged over the radar volume, as well as the variance and flux components , where refers to the fluctuating eastward wind, refers to the fluctuating northward wind, and refers to the fluctuating vertical wind. Data from radars in New Mexico and Resolute Bay are used to illustrate the data quality, and demonstrate theoretically expected seasonal forcing. Keywords. Meteorology and atmospheric dynamics (Middle atmosphere dynamics; Waves and tides; Climatology)

scholarly journals Tropical Cyclone Outflow-Layer Structure and Balanced Response to Eddy Forcings

2017 ◽  
Vol 74 (1) ◽  
pp. 133-149 ◽  
Author(s):  
Sarah D. Ditchek ◽  
John Molinari ◽  
David Vollaro
Keyword(s):  
Heat Flux ◽  
Tropical Cyclone ◽  
Momentum Flux ◽  
Layer Structure ◽  
Secondary Circulation ◽  
Intensity Change ◽  
Upper Troposphere ◽  
Eddy Heat Flux ◽  
Momentum Fluxes

Abstract The ERA-Interim is used to generate azimuthally averaged composites of Atlantic basin tropical cyclones from 1979 to 2014. Both the mean state and the eddy forcing terms exhibited similar radial–vertical structure for all storm intensities, varying only in magnitude. Thus, only major hurricanes are described in detail. Radial inflow and outflow extended beyond the 2000-km radius. Warm anomalies reached 2000 km in the outflow layer. Composite eddy momentum fluxes within the outflow layer were 2.5 times larger than mean momentum fluxes, highlighting the importance of outflow–environment interactions. A balanced vortex equation was applied to understand the role of eddy heat and momentum fluxes. Dominant terms were the lateral eddy heat flux convergence, lateral eddy momentum flux, and eddy Coriolis torque. Each acted to enhance the secondary circulation. The eddy momentum flux terms produced about twice the response of heat flux terms. The circulation created by the eddy Coriolis torque arises from a vertical gradient of mean storm-relative meridional wind in the upper troposphere at outer radii. It is produced by background inertial stability variations that allow stronger outflow on the equatorward side. Overall, the fluxes drive a strengthened secondary circulation that extends to outer radii. Balanced vertical motion is strongest in the upper troposphere in the storm core. A method is proposed for evaluating the role of environmental interaction on tropical cyclone intensity change.

Correlations for the Choked Mass and Momentum Flux Density Considering Real-Gas Thermodynamics

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Matthias Banholzer ◽  
Michael Pfitzner
Keyword(s):  
Flux Density ◽  
Mass Flux ◽  
Momentum Flux ◽  
Second Phase ◽  
Cfd Simulations ◽  
Choked Flow ◽  
Saturation Properties ◽  
Isentropic Flow ◽  
Computational Fluid Dynamics Cfd ◽  
Reduced Pressures

The choked mass flux density and the choked momentum flux density for the nonideal fluids methane and nitrogen have been calculated using the Soave–Redlich–Kwong equation of state (EoS). For the computation a steady, one-dimensional (1D), isenthalpic and isentropic flow is assumed. The developed algorithm for the calculation of the choked flow properties includes a bounded multidimensional Newton method. A possible second phase emerging in the critical nozzle area is excluded using the saturation properties of the considered fluids. The critical ratios of pressure, density, temperature, and speed of sound are discussed and compared to other publications. Formulations of the choked mass flux density and the choked momentum flux density explicit in Tr, pr, and Zr are given valid for different reduced pressures and temperatures depending on the fluid. Additional computational fluid dynamics (CFD) simulations are carried out in order to validate the findings of the algorithm and the proposed correlations.

Non-Boussinesq Integral Model for Horizontal Turbulent Strongly Buoyant Plane Jets

2008 ◽  
Author(s):  
Jianjun Xiao ◽  
John R. Travis ◽  
Wolfgang Breitung
Keyword(s):  
Power Plants ◽  
Boussinesq Approximation ◽  
Density Variation ◽  
Integral Model ◽  
Buoyant Jet ◽  
Boussinesq Model ◽  
Buoyant Jets ◽  
Jet Trajectory ◽  
Plane Jets ◽  
Hydrogen Safety

Horizontal buoyant jets are fundamental flow regimes for hydrogen safety analyses in the nuclear power plants. Integral model is an efficient, fast running engineering tool that can be used to obtain the jet trajectory, centerline dilution and other properties of the flow. In the published literature, most of the integral models that are used to predict the horizontal buoyant jet behavior employ the Boussinesq approximation, which limits the density range between the jets and the ambient. CorJet, a long researched, developed, and established commercial model, is such a Boussinesq model, and has proved to be accurate and reliable to predict the certain buoyant jet physics. In this study, Boussinesq and non-Boussinesq integral models with modified entrainment hypothesis were developed for modeling horizontal turbulent strongly buoyant plane jets. All the results and data where the Boussinesq model is valid will collapse to CorJet when they are properly normalized, which implies that the calculation is not sensitive to density variations in Boussinesq model. However, non-Boussinesq results will never collapse to CorJet analyses using the same normalized scaling, and the results are dependent on the density variation. The reason is that CorJet employs the Boussinesq approximation in which density variations are only important in the buoyancy term. For hydrogen safety analyses, the large density variation between hydrogen and the ambient, which is normally the mixture of air and steam, will make the Boussinesq approximation invalid, and the effect of the density variation on the inertial mass of the fluid can not neglected. This study highlights the assumption of the Boussinesq approximation as a limiting, simplified theory for strongly buoyant jets. A generalized scaling theory for horizontal strongly buoyant jet seems not to exist when the Boussinesq approximation is not applicable. This study also reveals that the density variation between jets and the ambient should be less than 10% to accurately model horizontal buoyant jets when the Boussinesq approximation is applied. Verification of this integral model is established with available data and comparisons over a large range of density variations with the CFD codes GASFLOW and Fluent. The model has proved to be an efficient engineering tool for predicting horizontal strongly buoyant plane jets.

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